According to the changelogs for the upcoming VaultWiki version 4.1.9:
Code:
Fixed Bug: missing inline edit control for tags on wiki content [in: XF >= 2.3]
I believe this was due to the icon changes in XenForo 2.3, where this particular icon may not render anymore. The changelog suggests there was a similar issue with categories.
Assuming you have permissions, you should still be able to edit the tags directly, by using the URL action ?do=tags
If you don't have permission, going to this action will show a permissions error.
Regarding the option you mentioned, I assume you're referring to Options > VaultWiki: Miscellaneous > Use forum tagging for wiki pages?
Which enables the XenForo tagging system for wiki content.
However, each wiki content type has permissions that need to be active for a user to be allowed to edit the tags.
For example, in Wiki > Permissions > Usergroup permissions, when editing a usergroup, under "Page permissions" there is a permission "Can tag wiki pages?"
There are similar settings for the various other content types.